1. Field of the Invention
This invention relates generally to a production method for manufacturing a large quantity of individually unique and distinct novelty glasses which may be either sunglasses or frames for prescription use. Hence, the invention specifically relates to a method for manufacturing either limited editions of sunglasses or limited edition pairs of eyeglass frames, each pair of sunglasses or frames having a random variety of sub-assemblies or components wherein at least two components are visually different or each pair of sunglasses or eyeglass frames having a random variety of shapes or colors for the sub-assemblies and/or sunglass lenses.
2. Description of the Prior Art
A prior art example of novelty glasses, not sunglasses, is shown in Rosenwinkel, et al, U.S. Pat. No. 4,283,127 issued on Aug. 11, 1981. Further, U.S. Pat. No. 4,798,455 issued on Jan. 17, 1989 to Yoe, et al is for a user reconfigurable pair of novelty glasses which includes separate temple pieces that may be readily combined with each other and with other separate eye frames and separate temple pieces by the user to form a variety of outrageously designed novelty sunglasses. Each eye frame may be used for either the users right or left eye and each temple piece and may be used over the users right or left temple and ear. However, the patent does not disclose or suggest a method for mass production of the unique novelty sunglasses disclosed.
The prior art production technology is shown first by U.S. Pat. No. 2,242,663, issued to Smith, on May 20, 1940 and assigned to Bausch and Lomb Optical Company. The Smith patent is directed to a new and improved means and method of setting up eyeglasses, spectacles, rimless mountings and lenses. Smith outlines the replacement of the screw in rimless mountings and the wide spread universal use of a rivet in its place and shows a new means for applying the rivets to rimless lenses. On Mar. 20, 1973, U.S. Pat. No. 3,721,275 was issued to Pforzheim of Germany for a process and apparatus for making polyconal spectacle glass rims. The invention was a process for manufacturing polyconal spectacles lens rims from profiled wire and a machine for carrying out the process. Pforzheim outlined that polyconal spectacles lens rims were previously made from profiled wire in a process in which the wire cut to length and prebent whereinafter a connector was applied and the rims were closed, then sized by being pulled several times over a shaped disk and subsequently subjected to meniscus bending in a die. That process was time-consuming. The Pforzheim invention sought to enable a more efficient manufacture of polyconal spectical glass rims which could be performed automatically.
U.S. Pat. No. 2,921,361 for a method for spectacle frame manufacture was issued to Buckner on Jan. 19, 1960 and assigned to American Optical Company. This invention disclosed improvements in machines for the manufacture of spectacle frames and was for an improved device for making the desired contour shape to the lens receiving portion of the frames. The invention provided a machine of simple construction in which the eye wires of a spectacle frame could be quickly and accurately shaped in an efficient and economical manner.
In many situations in manufacturing, a series of steps repeatedly occur which manufactures a product, for example eyeglasses. This manufacturing event is reproduced a large number of times as a production run under essentially the same conditions; yet the outcomes vary in an irregular manner that defies all attempts at prediction. Such situations give rise to a sequence of random events. Each event producing a slightly different object. In the prior art these objects were rejected. The novel invention utilizes the randomness of the outcomes of each production run to produce a quantity of individually unique products after each run.
Any product of a random production is termed an event. The event consists of any product with the properties E. Associated with a long sequence of random productions will be a number P(E), termed a probability, which gives the relative frequency of the occurrence of E.
The term probability thus used is associated with the outcome of a collection or sequence of random productions and is called a statistical probability.
Let a product be defined as the indecomposable outcome of a random production, e.g., eyeglasses. The product is composed of one or more sample properties E. The array of products (denoted by S) is defined as the aggregate of all the possible combinations of properties E. In the novel method, the properties E are defined by the number of choices N for each part of the eyeglasses. An event containing no properties of the sample space (denoted by 0) is called the null event. In point-set terminology, the spectrum S is a set. A property or part of the product is an element of the set. A group of properties E is a subset of S, and 0 is an empty set.
Let E.sub.1 and E.sub.2 be two properties in S. Then adopting the following operations from point-set theory:
1. E.sub.1 +E.sub.2 is the occurrence of at least one of the properties E.sub.1 or E.sub.2. PA1 2. E.sub.1 E.sub.2 is the simultaneous occurrence of the properties E.sub.1 and E.sub.2. PA1 3. E.sub.1 -E.sub.2 is the occurrence of products with a property E.sub.1 not common to E.sub.2.
These operations are both associative and distributive; however, only the sum and product operations are commutative. In particular, if two events contain no elementary points in common, they are said to be mutually exclusive events and E.sub.1 E.sub.2 =0.
Assume X.sub.1, X.sub.2 to be parts (of a product) of a (denumerable) sample space S, and let E.sub.1, E.sub.2, . . . be a collection of products which are subsets of S. Then the basic axioms of probability state that associated with every event E.sub.i is a real non-negative number termed a probability and denoted by P(E.sub.i) such that EQU 0.ltoreq.P(E.sub.i).ltoreq.1
If such product has a property E.sub.i and E.sub.i are all mutually exclusive events, then ##EQU1##
From the above axioms it follows that for any two products having properties E.sub.1 and E.sub.2 EQU P(E.sub.1 +E.sub.2)=P(E.sub.1)+P(E.sub.2)-P(E.sub.1 E.sub.2)
If a product with E can never occur in a sequence of random events, then E is called an impossible event and has the probability P(E)=0; similarly, if an event E will always occur at every run of a random production, E is called a certain product and has the probability P(E)=1. On the other hand, if an event E has a probability P(E)=0, this does not mean that the event E will never occur. All this means is that in a long sequence of random productions the relative frequency of E will be close to zero. This is precisely what the novel production method presented herein utilizes to produce a group of substantially unique eyeglasses. Similarly, if it is known that P(E)=1 for an event E, this does not mean that E will occur in every random production, but only that in a long sequence of productions the relative frequency will be close to 1.
For example, consider all numbers included within the interval (0, 1). If one number is drawn at random within this interval, the probability of drawing a rational number is equal to zero. Alternatively, the probability of drawing an irrational number will be equal to one.
The above discussion and relations define briefly the mathematical probability foundation for the method of manufacture of the novel invention where "relatively" unique objects are products of the method over a given production time at a given rate of production or a number of productions using the method. Further, two products with properties or features E.sub.1 and E.sub.2 are said to be distinct if the probability of the simultaneous occurrence of E.sub.1 and E.sub.2 is equal to the product of the individual probabilities; that is, if EQU P(E.sub.1 E.sub.2)=P(E.sub.1)P(E.sub.2)
If the product E.sub.2 does not exclude the production of the product E.sub.1, then some productions of E.sub.2 will also occur with productions of E.sub.1. The "relative frequency" of E.sub.1 in such cases is termed the conditional probability of E.sub.1 given E.sub.2, written as P(E.sub.1 /E.sub.2). If P(E.sub.2)=0, then ##EQU2## and if E.sub.1 and E.sub.2 are independent, then EQU P(E.sub.1 /E.sub.2)=P(E.sub.1) and P(E.sub.2 /E.sub.1)=P(E.sub.2)
which is an equivalent definition for independence, i.e., the probability of the product E.sub.1 does not depend upon the occurrence of E.sub.2, and vice versa.
More generally the independent occurrence of the events E.sub.1, E.sub.2, . . . , En is expressed by EQU P(E.sub.1 E.sub.2, . . . , En)
and the events E.sub.1, E.sub.2, . . . , En are said to be mutually independent if and only if EQU P(E.sub.1 E.sub.2, . . . , En)=P(E.sub.1)P(E.sub.2) . . . P(En)
A variable whose value depends on the outcome of a random production is termed a random (or stochastic) variable.
Associated with any one-dimensional random variable X, for example, one of the pairs of eyeglasses produced by the novel invention, is a unique distribution function (d.f.), F(x), defined as EQU F(x)=P(X.ltoreq.x)
where P(X.ltoreq.x) signifies the probability of the product "X.ltoreq.x". The probability that X takes on a value within the interval a.ltoreq.x.ltoreq.b is given by EQU P(a.ltoreq.X.ltoreq.b)=F(b)-F(a)
From the mathematical definition of probability it follows that (1) F(x) is a nondecreasing function of x, that is, EQU F(x.sub.1).ltoreq.F(x.sub.2) for x.sub.1 .ltoreq.x.sub.2
(2) F(x) is everywhere continuous on the right, EQU F(x)=lim F(x+e) where e approaches zero. EQU F(X)=1 where X approaches infinity.
Thus, the set (x.sub.s) of products for which P(X=X)&gt;0 is the spectrum of the random variable X, i.e., the number of unique products or objects to be produced by a stochastic production such as the novel method of the invention.